Learning Koopman Models From Data Under General Noise Conditions
For researchers in nonlinear system identification and control, this work provides a statistically consistent and computationally efficient method to learn Koopman models from noisy data, addressing a known bottleneck in handling process and measurement noise.
This paper proposes a novel method for learning Koopman models from input-output data under general noise conditions, achieving statistical consistency and efficient batch optimization via multiple-shooting. The approach is validated on nonlinear benchmarks and a Crazyflie 2.1 quadcopter, demonstrating excellent long-term prediction.
This paper presents a novel identification approach of Koopman models of nonlinear systems with inputs under rather general noise conditions. The method uses deep state-space encoders based on the concept of state reconstructability and an efficient multiple-shooting formulation of the squared loss of the prediction error to estimate the dynamics and the lifted state only from input-output data. Furthermore, the Koopman model structure includes an innovation noise term that is used to handle process and measurement noise. It is shown that the proposed approach is statistically consistent (estimation error tends to zero when the number of data points goes to infinity) and computationally efficient due to the multiple-shooting formulation, by which the prediction error of the model can be calculated on multiple subsections of the data in parallel. The latter allows for efficient batch optimization of the network parameters and, at the same time, excellent long-term prediction capabilities of the obtained models. The performance of the approach is illustrated by nonlinear benchmark examples and experimental data from a Crazyflie 2.1 quadcopter.